A QUASICONFORMAL ANALOG OF CARATHéODORY’S CRITERION FOR THE M?BIUS PROPERTY OF MAPPINGS

摘要

In 1937, Carathéodory proved that every injective mapping f: G → f(G) ? C of a domain G ? C, taking circles to circles, is M?bius. The present article shows that if each injective mapping takes circles onto k-quasicircles then it is K-quasiconformal with K ≤ k +√k2 ? 1.